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Coefficient estimates and Landau-Bloch’s constant for planar harmonic mappings. (English) Zbl 1216.31001
Summary: The aim of this paper is to study the properties of planar harmonic mappings. The main results are as follows. First, by using the subordination of analytic functions, a sharp coefficient estimate is obtained and several applications are given. Then two results about Landau-Bloch’s constant are proved: one for planar harmonic mappings and the other for L(f), where L represents the linear complex operator L=z z-z ¯ z ¯ defined on the class of complex-valued C 1 functions in the plane, and f is an open harmonic mapping.
31A05Harmonic, subharmonic, superharmonic functions (two-dimensional)
30C45Special classes of univalent and multivalent functions